Dynamical Electroweak Breaking and Latticized Extra Dimensions

TL;DR

The paper develops a gauge-invariant, renormalizable 1+3D effective Lagrangian that captures a remodeled 1+4D Standard Model with latticized extra dimensions and warped backgrounds. It shows that dynamical electroweak symmetry breaking via Topcolor and Top Seesaw arises naturally, with vectorlike quarks emerging as bulk remnants and a composite Higgs appearing at the TeV scale. The framework yields a CKM flavor structure and radiative mass generation for light generations, and it accommodates a viable 4th generation and neutrino seesaw scenarios. This remodeled extra-dimensional approach provides a systematic platform for flavor dynamics beyond the Standard Model, linking higher-dimensional physics to observable phenomenology while noting the need for detailed constraint analyses in future work.

Abstract

Using gauge invariant effective Lagrangians in 1+3 dimensions describing the Standard Model in 1+4 dimensions, we explore dynamical electroweak symmetry breaking. The Top Quark Seesaw model arises naturally, as well as the full CKM structure. We include a discussion of effects of warping, and indicate how other dynamical schemes may also be realized.

Figures (12)

• Figure 1: A left-handed chiral zero mode $T_L$ (right-handed $t_R$) is localized on brane 1, by coupling to a kink in a background field $\varphi(x^5)$ which gives a negative (positive) Dirac mass to the right of brane 1 and negative (positive) to the left of brane 1. We denote the negative (positive) Dirac mass by the up-arrow (down-arrow) curved links on each brane. The trapping Dirac mass, with a coarse grain lattice, can alternatively be added to link terms on one side of the zero-mode as in Appendix B. We use the definition of the derivative for $T_L$ with linking Higgs fields with $L,j-1$ hopping to $R,j$, represented by the diagonal links between nearest neighbor branes, and $\sim -\overline{T}_{R,j}T_{L,j}$ are vertical links on a given brane eq.(B.2). For $t_R$ we use the definition eq.(B.1). We keep only the lowest lying vectorlike modes in the picture.
• Figure 2: A condensate $\left\langle \overline{T}_Lt_R\right\rangle$ forms on brane 1 when the $SU(3)_1$ coupling constant $\tilde{g}_{3,1}$ is supercritical. This can be triggered from $\varphi(x^5)(G_{\mu\nu}^2)$ in the $1+4$ underlying theory, but is a free parameter choice in the $1+3$ effective Lagrangian.
• Figure 3: Two brane approximation. In the limit that $T_2$ decouples this is just the original Top Seesaw Model of topseesaw.
• Figure 4: Three brane approximation incorporating charm, where $C =(c,s)_L$ is a doublet zero-mode, and $c=c_R$ is a singlet zero mode, both trapped on brane 1 (we assume the vectorlike partners of $C$ and $c$ are decoupled). The Dirac flavor mixing between $\overline{C}_L T_{R1}$ and $\overline{c}_Rt_{L1}$ can be rotated away by redefinitions of $T_{R1}$ and $t_{L1}$.
• Figure 5: The flavor mixing (dashed lines) between $\overline{C}_L\prod(\Phi/v) T_{R2}$ and $\overline{c}_R\prod(\Phi/v) t_{L2}$ cannot be rotated away by redefinitions of $T_{R2}$ and $t_{L2}$ without generating effective kinetic term mixing which leads to non-zero-mode flavor changing gluon vertices (in the broken phase where $\Phi\rightarrow v$; this mixing is actually a higher dimension operator). The charm quark mass is thus generated when radiative corrections are included (wavy line).